Question

Please solve this, pls ignore the marked words with a line :)

Answer 1

ANSWER:

$\begin{gathered} 4\cdot\frac{1}{2}\cdot(x-2)=(y-1)^2 \\ \text{ Focus }=(\frac{5}{2},1) \\ \text{ Vertex = }(2,1) \\ \text{ Directrix = }\frac{3}{2} \end{gathered}$

STEP-BY-STEP EXPLANATION:

We have the following function:

$-2x+y^2-2y+5=0$

We convert it to its standard form as follows:

$\begin{gathered} 2x=y^2-2y+5 \\ x=\frac{y^2}{2}-\frac{2y}{2}+\frac{5}{2} \\ x=\frac{1}{2}\cdot(y-1)^2+2 \\ 2\cdot(x-2)=(y-1)^2 \\ 4\cdot\frac{1}{2}\cdot(x-2)=(y-1)^2 \end{gathered}$

Now, starting from the standard form, we can define the focus, the vertex and the directrix:

$\begin{gathered} \text{ Focus }=(\frac{5}{2},1) \\ \text{ Vertex = }(2,1) \\ \text{ Directrix = }\frac{3}{2} \end{gathered}$